Multivariate position estimation

1. A method, performed by a tracker that comprises a computing system that is configured to receive periodic communications from a moving object and employ various types of information derived from the periodic communications to estimate a position of the moving object, the computing system comprising one or more computing devices, for performing multivariate position estimation to track the moving object with high accuracy, the method comprising: receiving periodic communications emitted from a moving object; processing each of the periodic communications to generate a time of arrival measurement, an angle of arrival measurement, and a Doppler measurement for each respective periodic communication; obtaining a tracker location representing where the tracker was located when each respective periodic communication was received; and tracking the moving object by iteratively estimating an object location representing where the moving object was located when the moving object emitted each respective periodic communication using the time of arrival measurement, the angle of arrival measurement, the Doppler measurement, and the tracker location for the respective periodic communication, wherein the tracker estimates the object location for the respective periodic communication by minimizing a cost function that includes: a time of arrival portion that incorporates the time of arrival measurement for the respective periodic communication; an angle of arrival portion that incorporates the angle of arrival measurement for the respective periodic communication; a Doppler portion that incorporates the Doppler measurement for the respective periodic communication; and a tracker location portion that incorporates the tracker location when the respective periodic communication was received.

2. The method of claim 1 , wherein the time of arrival portion comprises: τ o ⁢ b ⁢ s -  A ⁢ B → ^  c - τ e σ τ where A represents the object location, B is the tracker location, τ obs is the time of arrival measurement, c is the speed of light, τ e is an emission time of the respective periodic communication, and σ τ is a standard deviation of a time of arrival component that generated the time of arrival measurement.

3. The method of claim 2 , wherein the time of arrival measurement is a time difference of arrival measurement.

4. The method of claim 1 , wherein the angle of arrival portion comprises: θ - φ σ φ where θ is defined as a four quadrant arctangent function of a two dimensional x, y plane between A and B where A represents the object location and B is the tracker location, φ is the angle of arrival measurement, and σ φ is a standard deviation of an angle of arrival component that generated the angle of arrival measurement.

5. The method of claim 1 , wherein the Doppler portion comprises f d ⁢ m + f c - f e -  A ⁢ B → ^  · V → λ σ δ . where σ {dot over (δ)} is a standard deviation of a Doppler component that generated the Doppler measurement, f dm is the Doppler measurement, f c is a carrier frequency of the respective communication, f e is a measured frequency error, and V is a velocity of the tracker.

7. The method of claim 1 , wherein minimizing the cost function comprises performing a non-linear least squares algorithm.

8. The method of claim 7 , wherein the non-linear least squares algorithm is the Levenberg-Marquardt algorithm.

9. The method of claim 1 , wherein the tracker includes multiple nodes each of which receives and processes the periodic communications to generate respective time of arrival measurements, angle of arrival measurements, and Doppler measurements for each of the respective communications and each of which obtains a tracker location pertaining to the respective node, and wherein the moving object is tracked by iteratively estimating the object location representing where the moving object was located when the moving object emitted each respective periodic communication using the time of arrival measurements, the angle of arrival measurements, the Doppler measurements and the tracker locations.

10. A tracker for performing multivariate position estimation to track a moving object with high accuracy, the tracker comprising a computing system that is configured to receive periodic communications from a moving object and employ various types of information derived from the periodic communications to estimate a position of the moving object, the computing system comprising one or more computing devices, the tracking including: one or more antennas for receiving the periodic communications emitted from the moving object; a time of arrival component that generates a time of arrival measurement for each respective periodic communication; an angle of arrival component that generates an angle of arrival measurement for each respective periodic communication; a Doppler component that generates a Doppler measurement for each respective periodic communication; a tracker location component that obtains a tracker location representing where the tracker was located when each respective periodic communication was received; and a location engine that receives and processes the time of arrival measurement, the angle of arrival measurement, the Doppler measurement, and the tracker location for each respective periodic communication to iteratively estimate an object location representing where the moving object was located when the moving object emitted the respective periodic communication, wherein the location engine estimates the object location for the respective periodic communication by minimizing a cost function that includes: a time of arrival portion that incorporates the time of arrival measurement for the respective periodic communication; an angle of arrival portion that incorporates the angle of arrival measurement for the respective periodic communication; a Doppler portion that incorporates the Doppler measurement for the respective periodic communication; and a tracker location portion that incorporates the tracker location when the respective periodic communication was received.

11. The tracker of claim 10 , wherein the time of arrival portion comprises: τ o ⁢ b ⁢ s -  A ⁢ B → ^  c - τ e σ τ where A represents the object location, B is the tracker location, τ obs is the time of arrival measurement, c is the speed of light, τ e is an emission time of the respective periodic communication, and σ τ is a standard deviation of the time of arrival component.

12. The tracker of claim 10 , wherein the angle of arrival portion comprises: θ - φ σ φ where θ is defined as a four quadrant arctangent function of a two dimensional x, y plane between A and B where A represents the object location and B is the tracker location, φ is the angle of arrival measurement, and σ φ is a standard deviation of the angle of arrival component.

13. The tracker of claim 10 , wherein the Doppler portion comprises f d ⁢ m + f c - f e -  A ⁢ B → ^  · V → λ σ δ . where σ {dot over (δ)} is a standard deviation of the Doppler component, f dm is the Doppler measurement, f c is a carrier frequency of the respective periodic communication, f e is a measured frequency error, and V is a velocity of the tracker.

15. The tracker of claim 10 , wherein the tracker includes multiple nodes each of which includes: one or more antennas for receiving the periodic communications emitted from the moving object; a time of arrival component that generates a time of arrival measurement for each respective periodic communication received at the respective node; an angle of arrival component that generates an angle of arrival measurement for each respective periodic communication received at the respective node; a Doppler component that generates a Doppler measurement for each respective periodic communication received at the respective node; and a tracker location component that obtains a tracker location representing where the respective node of the tracker was located when each respective periodic communication was received at the respective node; and wherein the location engine receives and processes the time of arrival measurements, the angle of arrival measurements, the Doppler measurements, and the tracker locations from each node to iteratively estimate the object location representing where the moving object was located when the moving object emitted each respective periodic communication.

16. A method, performed by a tracker that comprises a computing system that is configured to receive periodic communications from a moving object and employ various types of information derived from the periodic communications to estimate a position of the moving object, the computing system comprising one or more computing devices, for performing multivariate position estimation to track the moving object with high accuracy, the method comprising: receiving periodic communications emitted from a moving object; processing each of the periodic communications to generate a time of arrival measurement, an angle of arrival measurement, and a Doppler measurement for each respective periodic communication; obtaining a tracker location representing where the tracker was located when each respective periodic communication was received; and tracking the moving object by iteratively estimating an object location representing where the moving object was located when the moving object emitted each respective periodic communication using the time of arrival measurement, the angle of arrival measurement, the Doppler measurement, and the tracker location for the respective periodic communication, wherein the tracker estimates the object location for the respective periodic communication by minimizing a cost function that includes: a time of arrival portion that incorporates the time of arrival measurement for the respective periodic communication; an angle of arrival portion that incorporates the angle of arrival measurement for the respective periodic communication; a Doppler portion that incorporates the Doppler measurement for the respective periodic communication; and a tracker location portion that incorporates the tracker location when the respective periodic communication was received; wherein the tracker location is one of fixed or moving.